A particle of mass m = 1 kg is dropped from a height h = 40 cm on a light horizontal platform fixed to one end of an elastic spring, the other being fixed to a base, as shown in the diagram. The particle collides with the platform and sticks to it. As a result, the spring is compressed by an amount x = 10 cm . What is the force constant of the spring? (Take g = 10 m s - 2 )

Step-by-step solution

Since the platform is depressed by an amount x, the total work done on the spring is m g ( h   +   x ) . This work is stored in the spring in the form of potential energy 1 2 k x 2 . Equating the two, we have 1 2 k x 2 = m g h + x or k = 2  mg h + x x 2 Given, h   =   0 . 4   m , x   =   0 . 1   m , m   =   1   kg and g   =   10   m   s - 2 . Substituting these values, we get k   =   1000   N   m - 1 .